Impossible to cut terrain surface with knife project tool
I tried your STL file, imported (and scaled it down to the grid size, about .0001) then recalculated normals (face normals pointing up to +Z). 

Then added a simple plane (4 verts, face normal points up to +Z)

Placed the plane somewhat above the STL map



then selected the plane, and after also the map, entered edit mode and from ortho top view uset "knife project":



after hiding the plane:



imho, it should work, in this way...